{"title":"Traveling edge states in massive Dirac equations along slowly varying edges","authors":"Pipi Hu, Peng Xie, Yi Zhu","doi":"10.1093/imamat/hxad015","DOIUrl":null,"url":null,"abstract":"\n Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling wave solutions to the two-dimensional Dirac equation with a domain wall mass in this work. It is known that the system admits exact and explicit traveling wave solutions, which are termed edge states if the interface is a straight line. By modifying such explicit solutions, we construct quasi-traveling-wave solutions if the interface is nearly straight. The approximate solutions in two scenarios are given. One is the circular edge with a large radius, and the second is a straight line edge with the slowly varying along the perpendicular direction. We show the quasi-traveling wave solutions are valid in a long lifespan by energy estimates. Numerical simulations are provided to support our analysis both qualitatively and quantitatively.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imamat/hxad015","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 7
Abstract
Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling wave solutions to the two-dimensional Dirac equation with a domain wall mass in this work. It is known that the system admits exact and explicit traveling wave solutions, which are termed edge states if the interface is a straight line. By modifying such explicit solutions, we construct quasi-traveling-wave solutions if the interface is nearly straight. The approximate solutions in two scenarios are given. One is the circular edge with a large radius, and the second is a straight line edge with the slowly varying along the perpendicular direction. We show the quasi-traveling wave solutions are valid in a long lifespan by energy estimates. Numerical simulations are provided to support our analysis both qualitatively and quantitatively.
期刊介绍：
The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered.
The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
